Zheng defeated Olga Puchkova 6-1, 6-3 by finishing off six of her nine break opportunities. Zheng limited Puchkova to 38 percent of the points when Puchkova served.
Alexandra Dulgheru claimed a 6-7 (4-7), 6-2, 6-2 upset of fifth-seeded Lesia Tsurenko, with three breaks in each of the second and third sets, and Johanna Konta ousted eighth-seeded Lauran Davis 6-4, 4-6, 6-3.
Third-seeded Lourdes Dominguez Lino had little trouble in a 6-2, 6-2 victory over Chan Yung-Jan that took 57 minutes. She did drop her serve twice but also amassed six breaks in eight receiving games.
No. 4-seeded Yvonne Meusburger was even more dominant, winning nearly three-quarters of the points in dispatching Richel Hogenkamp 6-0, 6-1 in 46 minutes and seventh-seeded Yaroslava Shvedova got by Timea Babos 6-1, 2-6, 6-2.
Also winning Monday were Katarzyna Piter, Zheng Saisai, Petra Cetkovska and Zhang Shuai.
The formal name of the tournament is the Yinzhou Bank Cup International Women's Tennis Open.
Interpol investigating stolen passports on missing flight
Susan Sarandon 'very excited' about daughter's pregnancy